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I am trying to teach myself some computational neuroscience and am reading through the following textbook: https://www.oxcns.org/b6_text.html.

I'm finding this diagram confusing in particular c). My understanding is that the vertical bar is the cell membrane and the perpendicular connections to it are the connecting axon/synapse. This makes it look like the cell membrane has a connection coming out of it and connecting back to it. This can't be right, or is it?enter image description here

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From Wikipedia submitted by Fabuio here's a tracing of a pyramidal neuron, a type found in neocortex:

Pyramidal neuron

Red is a tracing of the dendrites of the cell, blue is the axon. Generally, cells get input on their dendrites and send outputs via the axon.

The "cell membrane" isn't really shown here or in your diagram, but each of these lines represents a roughly cylindrical structure where the outside is comprised of a ring of membrane with the inside of the cell in the center.

Your network diagrams have simplified the "red" input-receiving part to be just a single vertical line, yes. The architecture in (c) includes self-connections, yes: it depicts 4 "cells" that receive external input and input from themselves and each of the other 3 cells, and additionally have output going someplace else. Words used for this type of self-connection include "autapse" for the physical connection, and "recurrent" for the cyclical pattern, though recurrent connections need not be direct (e.g., A to B to C to A is also a recurrent pathway from the perspective of A).

I don't know why the author used a different diagram structure for these pseudo-pyramidal in panels a-d; perhaps it's because they originate in different sources, but the "open triangle with an upward stick" in (a), "closed triangle with upward stick" in (b), and "almost a triangle with a fat stick" in (c) and (d) are all representing the same thing, the important differences in the different architectures only involve what is connected to what.

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